Finite-dimensional differential algebraic groups and the Picard-Vessiot theory
Banach Center Publications, Tome 58 (2002) no. 1, p. 189.

Voir la notice de l'article dans European Digital Mathematics Library

We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear algebraic group over K) associated to the linear differential equation ∂Y = AY over K, when equipped with its natural connection ∂ - [A,-], is K-split just if it is commutative.
Classification : 34M60, 12H05
Mots-clés : Picard-Vessiot extension, differential Galois extension 
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     author = {Anand  Pillay},
     title = {Finite-dimensional differential algebraic groups and the {Picard-Vessiot} theory},
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Anand  Pillay. Finite-dimensional differential algebraic groups and the Picard-Vessiot theory. Banach Center Publications, Tome 58 (2002) no. 1, p. 189. https://geodesic-test.mathdoc.fr/item/BCP_2002__58_1_282107/